Topological and Variational Methods
in Nonlinear Analysis
TVMNA'2003
Scientific Committee
and Organizers
Topics
Announcements
About the Conference
Proceedings
Proceedings of the TVMNA'2003 conference will be published in the journal Topological Methods in Nonlinear Analysis, issued by the Juliusz Schauder Center for Nonlinear Studies of the Nicolaus Copernicus University of Torun.
The aim of the conference
Our purpose is to bring together outstanding mathematicians from many continents for giving expositional lectures concerning recent achievements in nonlinear analysis, exchanging scientific information as well as working out new methods and ideas in that area of mathematics.
Organization and management
The meeting will have a traditional, routine scheme of mathematical conference.
- Morning activities will consists of three one-hour lectures given by the invited speakers in two parallel sessions.
- For each day afternoon are scheduled two half of an hour talks delivered by the remaining participants of the meeting in three parallel sessions.
- Evening time is reserved for direct discussions and exchange of information and short seminars in small groups.
- Every participant, including young scientist will have an opportunity to present his (her) results at least during a poster session.
- The participants will be asked to submit papers to a volume of the proceedings of the conference.
The introducing of topological methods to the functional analysis led to the origin of nonlinear analysis - the field of mathematics, which has been developing fast and gets a growing importance with respect to connections with other parts of mathematics and other sciences.
Nonlinear problems appear in the theoretical mathematics (differential equations, differential geometry, dynamical systems) also in applied mathematics (optimal and control theory), but also in many nature sciences (mechanics, quantum physics, chemistry, biology, biophysics). A use of the nonlinear modes in the economy is important from the point of view of applications.
Mentioned in the title topological and variational methods have qualitative character i.e. they study the existence, multiplicity, continuation, bifurcation and a general form of solutions of nonlinear problems.
This conference will focus on topological and variational methods that are important with respect to applications in ordinary and partial differential equations and dynamical systems, and consequently significant to the applied mathematics. An international committee working in collaboration with the European Union of Mathematicians approved it to the schedule of official events at the Banach Centre.
It is a continuation of several earlier conferences, and workshops, under the same title (or with adjectives "singular" and "variational" added) organised at the Banach Centre in Warsaw or The Universities of Gdańsk and Poznań.
This time the aim is to concentrate on the variational methods mainly, but also a presentation of the variety of topics on the topological methods due a remarkable progress made recently. In particular the following topics will be included:
- Existence, bifurcation and continuation of periodic solutions od Hamiltonian systems via degree for SO(2)-equivariant gradient maps. Applications to Hamiltonian systems of celestial mechanics. The restricted 3-body problem.
- Homoclinic and heterocliic solutions of Hamiltonian systems via variational methods.
- Floer cohomology. Invariants of the symplectic structures. Fixed points of maps preservinga symplectic structure. Lusternik-Schnirelman symplectic category.
- Classical and infinite-dimensional Conley index and its applications to differential equations.
- Classical mini-max variational methods with applications to differential equations.
- Equivariant topological methods in variational problems with a symmetry. The existence and multiplicity of solutions. Symmetry breaking of solutons of nonlinear equivariant problems.
- Topological methods applied to General Relativity - Lorentz geometry.
- Spectral properties of linear differential operators that are essential for nonlinear problems.
- Computational approach to nonlinear analysis based in topological methods.